IEVref: | 103-03-06 | ID: | |

Language: | en | Status: Standard | |

Term: | unit doublet | ||

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Symbol: | δ′ | ||

Definition: | distribution being the derivative of the Dirac function Note 1 to entry: The unit doublet can be used to express the value for ${f}^{\prime}({x}_{0})=-{\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}{\delta}^{\prime}(x-{x}_{0})f(x)\mathrm{d}x$ | ||

Publication date: | 2009-12 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO | ||

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Note 1 to entry: The unit doublet can be used to express the value for *x*_{0} of the derivative of a function *f*(*x*) differentiable at $x={x}_{0}$:

${f}^{\prime}({x}_{0})=-{\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}{\delta}^{\prime}(x-{x}_{0})f(x)\mathrm{d}x$